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Semantics64

Exec64-mulh

Semanics of the MULH instruction [ISA:13.1].

Signature
(exec64-mulh rd rs1 rs2 stat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; stat — Guard (state64p stat).
Returns: new-stat — Type (state64p new-stat).

We read two signed 64-bit integers from rs1 and rs2. We multiply them, we shift the product right by 64 bits, and we write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec64-mulh

(defun exec64-mulh (rd rs1 rs2 stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (state64p stat))))
  (let ((__function__ 'exec64-mulh))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read64-xreg-signed rs1 stat))
         (rs2-operand (read64-xreg-signed rs2 stat))
         (product (* rs1-operand rs2-operand))
         (result (ash product 64))
         (stat (write64-xreg rd result stat))
         (stat (inc64-pc stat)))
      stat)))

Theorem: state64p-of-exec64-mulh

(defthm state64p-of-exec64-mulh
  (b* ((new-stat (exec64-mulh rd rs1 rs2 stat)))
    (state64p new-stat))
  :rule-classes :rewrite)

Theorem: exec64-mulh-of-ubyte5-fix-rd

(defthm exec64-mulh-of-ubyte5-fix-rd
  (equal (exec64-mulh (ubyte5-fix rd)
                      rs1 rs2 stat)
         (exec64-mulh rd rs1 rs2 stat)))

Theorem: exec64-mulh-ubyte5-equiv-congruence-on-rd

(defthm exec64-mulh-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec64-mulh rd rs1 rs2 stat)
                  (exec64-mulh rd-equiv rs1 rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-mulh-of-ubyte5-fix-rs1

(defthm exec64-mulh-of-ubyte5-fix-rs1
  (equal (exec64-mulh rd (ubyte5-fix rs1)
                      rs2 stat)
         (exec64-mulh rd rs1 rs2 stat)))

Theorem: exec64-mulh-ubyte5-equiv-congruence-on-rs1

(defthm exec64-mulh-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec64-mulh rd rs1 rs2 stat)
                  (exec64-mulh rd rs1-equiv rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-mulh-of-ubyte5-fix-rs2

(defthm exec64-mulh-of-ubyte5-fix-rs2
  (equal (exec64-mulh rd rs1 (ubyte5-fix rs2)
                      stat)
         (exec64-mulh rd rs1 rs2 stat)))

Theorem: exec64-mulh-ubyte5-equiv-congruence-on-rs2

(defthm exec64-mulh-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec64-mulh rd rs1 rs2 stat)
                  (exec64-mulh rd rs1 rs2-equiv stat)))
  :rule-classes :congruence)

Theorem: exec64-mulh-of-state64-fix-stat

(defthm exec64-mulh-of-state64-fix-stat
  (equal (exec64-mulh rd rs1 rs2 (state64-fix stat))
         (exec64-mulh rd rs1 rs2 stat)))

Theorem: exec64-mulh-state64-equiv-congruence-on-stat

(defthm exec64-mulh-state64-equiv-congruence-on-stat
  (implies (state64-equiv stat stat-equiv)
           (equal (exec64-mulh rd rs1 rs2 stat)
                  (exec64-mulh rd rs1 rs2 stat-equiv)))
  :rule-classes :congruence)